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A373575
Numbers k such that k and k-1 both have at least two distinct prime factors. First element of the n-th maximal antirun of non-prime-powers.
23
1, 15, 21, 22, 34, 35, 36, 39, 40, 45, 46, 51, 52, 55, 56, 57, 58, 63, 66, 69, 70, 75, 76, 77, 78, 85, 86, 87, 88, 91, 92, 93, 94, 95, 96, 99, 100, 105, 106, 111, 112, 115, 116, 117, 118, 119, 120, 123, 124, 130, 133, 134, 135, 136, 141, 142, 143, 144, 145
OFFSET
1,2
COMMENTS
The last element of the same antirun is given by A255346.
An antirun of a sequence (in this case A361102) is an interval of positions at which consecutive terms differ by more than one.
EXAMPLE
The maximal antiruns of non-prime-powers begin:
1 6 10 12 14
15 18 20
21
22 24 26 28 30 33
34
35
36 38
39
40 42 44
45
46 48 50
MATHEMATICA
Select[Range[100], !PrimePowerQ[#]&&!PrimePowerQ[#-1]&]
CROSSREFS
Runs of prime-powers:
- length A174965
- min A373673
- max A373674
- sum A373675
Runs of non-prime-powers:
- length A110969
- min A373676
- max A373677
- sum A373678
Antiruns of prime-powers:
- length A373671
- min A120430
- max A006549
- sum A373576
Antiruns of non-prime-powers:
- length A373672
- min A373575 (this sequence)
- max A255346
- sum A373679
A000961 lists all powers of primes. A246655 lists just prime-powers.
A057820 gives first differences of consecutive prime-powers, gaps A093555.
A356068 counts non-prime-powers up to n.
A361102 lists all non-prime-powers (A024619 if not including 1).
Various run-lengths: A053797, A120992, A175632, A176246.
Various antirun-lengths: A027833, A373127, A373403, A373409.
Sequence in context: A033708 A343821 A294171 * A306102 A177024 A325037
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jun 18 2024
STATUS
approved